According to Harald Cramér, "Filip Lundberg's works on risk theory were all written at a time when no general theory of stochastic processes existed, and when collective reinsurance methods, in the present sense of the word, were entirely unknown to insurance companies. In both respects his ideas were far ahead of their time, and his works deserve to be generally recognized as pioneering works of fundamental importance."
Filip Lundberg's father, Philip Lundberg, was a school teacher and Filip's first ambition was to follow his father's career. He studied mathematics at the University of Uppsala, graduating in 1896 and receiving his Licentiate in 1898. But, instead of becoming a teacher, Filip joined a newly founded insurance company. He soon moved to a second company where he was appointed actuary and at the age of 28 became its managing director. He went on to become a leader of the industry, managing other companies, serving as chairman of the Association of Swedish Life Insurance Companies for ten years and sitting on government committees on insurance.
In parallel to his business career Lundberg worked on a theory of collective risk. In 1903 he finished his doctoral thesis, Approximations of the Probability Function/Reinsurance of Collective Risks. This introduced the compound Poisson process and involved work on the central limit theorem. Cramér writes that the thesis has a reputation for being impossible to understand but, that looked at now, "one cannot help being struck by his ability to deal intuitively with concepts and methods that would have to wait another thirty years before being put on a rigorous foundation." Cramér mentions later work by Andrey Kolmogorov and William Feller but it was Cramér himself who developed Lundberg's ideas on risk and linked them to the emerging theory of stochastic processes.
Lundberg's ideas became known largely through the work of Cramér and his students. Although he published some work in German, the international scientific language of the time, Lundberg's thesis and most of his subsequent writings were in Swedish. His mathematical language did not travel easily, either.
- Cramér, H. (1969). "Historical review of Filip Lundberg's works on risk theory". Scandinavian Actuarial Journal 1969: 6–9. doi:10.1080/03461238.1969.10404602.
- K. Englund and A. Martin-Löf (2001) Ernst Filip Oskar Lundberg, Statisticians of the Centuries (ed. C. C. Heyde and E. Seneta) pp. 308–311. New York: Springer.